They're both good IMO. I think Eddie Bauer might be a bit younger/stylish in their look, and LL Bean is classic, sturdy and durable.
I used to buy from Eddie Bauer when they had a store in our mall. Now I don't have a place to make easy returns, so I don't shop with them.
LL Bean has free shipping for everyone, and Bean credit card holders get free return labels as well. I buy from them fairly often. I like their tees, jackets and sweaters.